How to stop my eye from watering?

Blockage or dry eye : One cause could be a nasolacrimal duct obstruction on that side. A history of trauma to the nose or no runny nose with the tearing might suggest this. It usually is pretty constant. Another cause could be dry eye. This might be accompanied by burning, tearing, light sensitivity or redness but not necessarily. It tends to fluctuate. I'd suggest trying some artificial tears four times a day.